Abstract
We study the Cauchy problem for the generalized Korteweg–de Vries (KdV) and one-dimensional fourth-order derivative nonlinear Schrödinger equations, for which the global well-posedness of solutions with small rough data in certain scaling limit of modulation spaces M 2 , 1 μ $\mathcal {M}_{2,1}^{\mu }$ is shown, which contain some data with infinite L2 norm.
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